Who cares?
It does not matter, as Vattel no longer controls the law on these issues.
As Madison stated, clearly, Congress had the authority to enact and change laws concerning citizenship.
Congress HAS changed the laws on citizenship, several times, since WKA was decided.
At the time of that antiquated MOOT ruling, there was little other guidance for the Court.
Now, there is, in the form of Congressional Legislation.
The rules to obtain Citizenship at Birth have changed over time. Natural Born Citizen means Citizen at Birth and NOTHING else!